A 2-coloring of [1,n] can have (n^2)/22 + O(n) monochromatic Schur triples, but not less!

Aaron Robertson; Doron Zeilberger

arxiv: math/9803149 · v2 · submitted 1998-03-30 · 🧮 math.CO · math.LO

A 2-coloring of [1,n] can have (n²)/22 + O(n) monochromatic Schur triples, but not less!

Aaron Robertson , Doron Zeilberger This is my paper

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keywords coloringmonochromaticschurtriplesasymptoticallyindependentlylessminimum

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We prove that the minimum number (asymptotically) of monochromatic Schur triples that a 2-coloring of [1,n] can have is (n^2)/22 + O(n). This was solved independently by Tomasz Schoen.

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A 2-coloring of [1,n] can have (n²)/22 + O(n) monochromatic Schur triples, but not less!

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